British Prime Minister Theresa May narrowly avoids a parliamentary defeat with Tuesday’s vote

LONDON—British Prime Minister Theresa May narrowly avoided a bruising parliamentary defeat Tuesday over her Brexit strategy, seeing off a challenge that would have given lawmakers much greater say over negotiations with Brussels.

Yet deep divisions remain in London over the terms of Britain’s withdrawal from the European Union, with several tricky issues still unresolved almost two years after voters chose to exit from the EU in a referendum.